The impetus for Beck’s latest project – a track-by-track cover of the 1967 recording “The Velvet Underground & Nico” — was the desire to get together with friends, play music they enjoyed and see if they could cut an entire album in a single day.

“It all began with an experiment to see what we could do in one day,” he told me when he called last night from his home in Los Angeles. “I was reading how the Beatles or Dylan — maybe it was “Meet the Beatles” — would record one track at nine, another at ten, then eleven and then there’d be a lunch break and then they’d do the rest of the album in the afternoon.”

Beck gathered friends to take on a spontaneous project. “It came down to three or four in the afternoon. Nobody could agree on what we should do.” Then the singer they’d intended to employ turned up ill. “Someone knew Thorunn Magnusdottir, who could sing. But we were running out of time.”

“The Velvet Underground & Nico,” Beck said, “was an obvious choice. Everybody was familiar with it. It took us a couple of minutes to figure out the songs.”

Largely written by Lou Reed, the original album’s production is credited to Andy Warhol, who introduced Nico to the band. Warhol designed the album’s cover and featured the group at his parties.

The band for Beck’s one-day session included his band mates Joey Waronker, Brian Lebarton and Bram Insocore; producer Nigel Godrich; actor Giovanni Ribisi, who is the twin brother to Beck’s wife Marissa; DJ Chris Holmes; and others. From Iceland, Magnusdottir is in the Nico role, though the recording isn’t an attempt to recreate the album note for note.

“It’s pretty faithful,” Beck admitted. Indeed, the opening track from the project, a lovely reading of “Sunday Morning,” was posted on www.beck.com yesterday, along with a video of the recording session. It’s an homage to the original, but not a recitation. Beck, not Magnusdottir, takes the lead on a vocal that was originally done by Nico.

He has a long history with the album –- a pre-history, in fact. His grandfather Al Hansen, an artist, was an influential figure at Warhol’s East Side Manhattan studio known as the Factory. Beck’s mother Bibbe Hansen was a Warhol protégé who appeared in several of his films. Finally, Beck often performed “Sunday Morning” in concert.

“I grew up listening to the Velvet Underground,” he said. “When I was fifteen, I was taken with trying to imitate Lou Reed.”

I mentioned to Beck that I found a similarity between his vocal delivery and Nico’s –- a sort of shared matter-of-factness. In Beck’s case, it comes across an earnest lack of affect, though early in his career it was ascribed to a slacker’s pose. With Nico, a former model, the delivery is influenced by a limited vocal range and her seemingly native insouciance.

Beck told me he found something vaguely troubling about covering an album from beginning to end. “There’s a presumptuousness,” he said, “but it’s only in the modern era where people recorded their own songs. There were always many, many interpretations of songs whether it was a jazz combo, an Andy Williams-type singer or a folk singer or a rock band.”

“By doing the whole album,” he added, “you get to do some of the lesser-known songs you would’ve never chosen to perform. You end up learning things.”

Beck said he wanted to get back to the simplicity of recording without the pressures of meeting a record label’s demands.

“One of the things about this was that we were just playing for ourselves and our friends.” That often isn’t the way once a career is launched, he said. “What happens is someone gets a record deal or goes on tour and certain parts of it becomes a job. Certain structures are imposed on you.

“My experience is that’s when quality suffers. It feels real when nobody knows the ‘record’ button’s been pushed, when they’re not prepared for it. Otherwise, artifice comes into play –- like the difference between how you look and how you look when someone’s taking a photo. It’s a human instinct. But when people aren’t ready, you get something genuine.

“The last few years I was thinking I wanted to do something for my own satisfaction,” he added. “You know, what would I do if I could do it for fun?”

His 2008 release, “Modern Guilt,” required overdubbing as Beck played a number of instruments. But, he said, “My favorite way to record is to play with a group of friends sitting around a room. So many things can go into planning a record that you can lose energy and emotion that you get in a live recording.”

Beck said he intends to issue a track a week via his revamped website. “The Velvet Underground & Nico” has 11 tracks, but the ad-hoc band recorded two versions of Reed’s “Heroin.” The second album in the series is already complete and Beck and friends are about to begin recording the third. He wouldn’t tell me what either was.

“I’m sure it’ll get out,” he said. “But I’d like to make it a surprise.”